Debt repayment strategies are often debated between focusing on the highest interest rate debt or the debt with the smallest balance. Economists recommend focusing on the highest interest rate debt to minimize costs, while proponents of the debt snowball method suggest focusing on the smallest debt for motivation. Dave Ramsey acknowledges the mathematical sub-optimality of the debt snowball method but emphasizes its effectiveness in maintaining motivation and behavior change, ultimately preventing giving up and incurring more costs in the long run.